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A new class of fuzzy implications. Axioms of fuzzy implication revisited

✍ Scribed by I. Burhan Türkşen; Vladik Kreinovich; Ronald R. Yager

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
387 KB
Volume
100
Category
Article
ISSN
0165-0114

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✦ Synopsis

Many different fuzzy implication operators have been proposed; most of them fit into one of the two classes: implication operations that are based on an explicit representation of implication A ---, B in terms of &, V, and ~ (e.g., S-implications that are based on the formula B V ~ A), and R-implications that are based on an implicit representation of implication A --, B as the weakest C for which C&B implies A. However, some fuzzy implication operations (such as h") cannot be naturally represented in this form. To describe such operations, we propose a new (third) class of implication operations called A-implications whose relation to &, V, and ~ is described by (implicit) axioms..

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